Question

In clinical studies, Inulin and para-amino hippuric acid given intraveneously until steady state is reached in a 70 kg man. Once steady state was reached, the following measurements were collected: arterial plasma concentration of inulin 0.18 mg/ml, of paraamino hippuric acid 0.21 mg/ml; renal venous plasma concentration of para-amino hippuric acid 0.0014 mg/ml; urine flow 2.2 ml/min; urinary concentration of inulin 11.0 mg/ml, of para-amino hippuric acid 5.5 mg/ml. Calculate the renal venous concentration of inulin.

Total Body Water = 42L

Extracellular Fluid = 14L

Osmolarity = 300mOsmoles/L

Intracellular Fluid = 28L

Answer 1

Inulin is a substance that is completely filtered but neither reabsorbed nor secreted in the tubular kidney and is therefore used to measure GFR (Glomerular Filtration Rate). Hence, the renal venous concentration of inulin is zero.

By, calculation, we get concentration of filtered inulin nearly equal to concentration of excreted urine, i.e, P_IN X C_IN = U_IN X V, where

P_IN = Plasma concentration of inulin

C_IN = Filtration rate of inulin (Nearly equal to standard GFR of 125 mL/min, slight variations will be present depending on person)

U_IN = Urine concentration of inulin

V = Urine flow rate

Applying values given in question above,

P_IN X C_IN = 0.18 X 125 = 22.5 mg/min

U_IN X V = 11 X 2.2 = 24.2 mg/min

Hence, we can see that LHS and RHS are nearly equal (slight variation due to personally variation in GFR from standard value), which proves that inulin is completely filtered and is neither reabsorbed or secreted and thus renal venous concentration of inulin is nearly zero.